Robert R. Stewart, Henry C. Bland, Qi Zhang*, and Felix Guthoff**

Transcription

1 Average versus interval Vp/Vs Average versus interval Vp/Vs Robert R. Stewart, Henry C. Bland, Qi Zhang*, and Felix Guthoff** *Matrix Geoservices Ltd., Calgary; **Institute für Geophysik, Münster, Germany ABSTRACT The average Vp/Vs value of a set of layers is a weighted sum of the interval Vp/Vs values. The weighting is the fractional transit time in the interval relative to the total traveltime across the set of layers. The average value is also bounded by the maximum and minimum interval values. The thicker a specific layer is or the more anomalous its Vp/Vs value, the greater is its influence on the average value. Two modeling results (for a porous dolomite case and a sand channel) indicate that average Vp/Vs analysis should be able to discern anomalous reservoir values. AVERAGE Vp/Vs VALUE OF MULTIPLE LAYERS In seismic analysis, we often extract a low-resolution or macroscopic parameter, such as average velocity, which is dependent on higher resolution values such as interval velocities. Thus, we may be interested in understanding how the microvalues effect the macro-parameters. In this case, how do P- and S-interval velocity ratios effect the average velocity ratio? Average versus interval velocities are of interest for several reasons: For example, when picking events and isochrons on P and S sections, we often take several cycles between picked events (Miller et al., 1996). This means that a series of layers are entering into the isochrons, isochron ratios and thus overall Vp/Vs calculation. The question is how does the overall or average Vp/Vs value relate to the interval Vp/Vs values? Furthermore, what size of interval value anomalies could be expected to make a significant contribution to the average value? Average Vp/Vs calculation Suppose that we have a layered medium (with layers i=1, N) having P-wave and S-wave interval velocities (α i,β i ). Each layer has thickness and a set of transit s times: t ip for one-way P waves and t i for one-way S waves (Figure 1). What is the average velocity ratio for the whole section? Let s first define an average Vp/Vs value as the ratio of average velocities (after Sheriff, 1984): γ Z T p, (1) Z Ts where Z is the total depth traveled, Tp is the one-way P-wave traveltime to depth Z, and Ts is the one-way S traveltime from Z to the surface, and then s But t i = γ i t p i, and γ = Ts T p. (2) CREWES Research Report Volume 9 (1997) 8-1

2 Stewart and Bland (3) (4) where or the fractional transit time. t i p t i s γ 1 = α 1 β 1 α 1, β 1 α 2, β 2 α j, β j Z α k, β k γ N = α N β N α N, β N Figure. 1. Plane-layer elastic medium with N layers. Thus, the average Vp/Vs value is the transit-time weighted sum of the interval velocity ratios. Furthermore, γ will be bounded by the minimum and maximum interval ratios ( γ i ) as shown below: 8-2 CREWES Research Report Volume 9 (1997)

3 Average versus interval Vp/Vs (5) (6) Thus, min (γ i ) γ max (γ i ). In addition, if there are small changes in and then (7) Note that if only changes (not the s), then (8) So if is, say, 0.2 and is 0.05 then needs to be about 0.25 (one-quarter of the total traveltime in the isochron). Examples Let s take several examples to show the effect of a variable velocity layer on the average Vp/Vs value. In the first case, the medium s velocities are given in Table 1. Figure 2 shows the results graphically. If the observable change in an average Vp/Vs value is say 0.05 and we have an interval ratio change of 1.9 to 1.7, then we need a layer of about 50 m thickness to be discernible. So, for an isochron ratio or average Vp/Vs determination across a thick stack of layers, 130 m in this case, a 10 m layer gives little impact. On the other hand, and as expected, a 50 m target layer has a sizable influence on the final Vp/Vs value. Table 1. Five-layer elastic model with variation in the third layer. Layer Thickness (m) Vp (m/s) Vs (m/s) Vp/Vs CREWES Research Report Volume 9 (1997) 8-3

4 Stewart and Bland Figure. 2. Variation of the average V p /V s value over the 5 layer model (Table 1) with changes in thickness (z3) and V p /V s value of the third layer. Two more examples, directly related to field cases are shown. We observe the effects of altering the reservoir thicknesses and Vp/Vs values for a Lousana Nisku case (Miller et al., 1996) and a Blackfoot sand channel example (Stewart et al., 1996) - both from Alberta. The reservoir of interest in the Lousana example is a 23 m porous dolomite unit. Analysis of well logs and seismic data in the area indicate that the Vp/V value drops from about 2.0 to 1.75 from the basinal anhydrite to the reservoir dolomite. In Table 2 and Figure 3, we see that a 10 m reservoir in an 80 m isopach will likely be difficult to resolve using isochron analysis, but a 20 m reservoir should be discernible. Logs in the Blackfoot, Alberta area indicate that P-wave velocities are about 4000 m/s in both reservoir sands and regional shales. The sand channels can be up to about 45 m thick. The S-wave velocity changes from about 2200 m/s to 2400 m/s from regional values to reservoir sandstone (Ferguson and Stewart, 1997). This provides a Vp/Vs change of about 1.9 to 1.7 from regional to reservoir units. Results from the Blackfoot model of Table 3 are shown in Figure 4. Again, if we assume that we can pick real variations in Vp/Vs down to about 0.05, then a Glauconitic sand with thickness greater than about 10 m in the 40 m isopach should produce an anomalous and measurable Vp/Vs value. 8-4 CREWES Research Report Volume 9 (1997)

5 Average versus interval Vp/Vs Table 2. Elastic values for intervals in the Lousana Nisku case. Layer Thickness (m) Vp (m/s) Vs (m/s) Vp/Vs Wabamun salt Calmar shale Nisku anhydrite Nisku porous dolomite Nisku tight dolomite Figure 3. Variation of the average V p /V s value with thickness and interval V p /V s from the Lousana Nisku model (Table 2). CREWES Research Report Volume 9 (1997) 8-5

6 Stewart and Bland Table 3. Elastic values for the Blackfoot sand channel model. Layer Thickness (m) Vp (m/s) Vs (m/s) Vp/Vs Mannville Glauconitic channel Basal quartz Figure. 4 Variation of the average V p /V s value with thickness and interval values from the Blackfoot sand channel model (Table 3). CONCLUSIONS The average Vp/Vs value of a set of layers is a weighted sum of the interval velocity ratios. The average value is also bounded by the maximum and minimum interval values. It will change according to changes in the target layer. The thicker the layer or more anomalous its Vp/Vs value, the greater its influence on the average value. Modeling for a porous dolomite reservoir and sand channel indicate that the reservoirs should be resolvable using average Vp/Vs values. 8-6 CREWES Research Report Volume 9 (1997)

7 REFERENCES Average versus interval Vp/Vs Miller, S.L.M., Harrison, M.P., Lawton, D.C., Stewart, R.R., Szata, K.J., 1996, Coupled P-P and P-S seismic interpretation of a carbonate reservoir: submitted to Geophysics. Sheriff, R.E., 1984, 2nd ed., Encyclopedic dictionary of exploration geophysics: Soc. Expl. Geophys. Stewart, R.R., Ferguson, R.J., Miller, S.L.M., Gallant, E., Margrave, G., 1996, The Blackfoot seismic experiments: Broad-band, 3C-3D, and 3-D VSP surveys: CSEG Recorder, 6, Ferguson, R.J. and Stewart, R.R., 1997, Sand/shale differentiation using shear-wave velocity from P- S seismic data: Submitted to the J. Seis. Explor. CREWES Research Report Volume 9 (1997) 8-7